Solve frac{(4sqrt{3})^2}{sqrt{3}}

$$\frac { ( 4 \sqrt { 3 } ) ^ { 2 } } { \sqrt { 3 } }$$

Evaluate

$$16\sqrt{3}\approx 27.712812921$$

Solution Steps

Expand \left(4\sqrt{3}\right)^{2}.

$$\frac{4^{2}\left(\sqrt{3}\right)^{2}}{\sqrt{3}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16\left(\sqrt{3}\right)^{2}}{\sqrt{3}}$$

The square of \sqrt{3} is 3.

$$\frac{16\times 3}{\sqrt{3}}$$

Multiply 16 and 3 to get 48.

$$\frac{48}{\sqrt{3}}$$

Rationalize the denominator of \frac{48}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{48\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{48\sqrt{3}}{3}$$

Divide 48\sqrt{3} by 3 to get 16\sqrt{3}.

$$16\sqrt{3}$$